ISTANBUL TECHNICAL UNIVERSITY « INSTITUTE OF SOCIAL SCIENCES
OPTIMAL ENVIRONMENTAL POLICY IN DIFFERENT MARKET STRUCTURES UNDER COOPERATIVE AND COMPETITIVE R&D
Master Thesis by Ilker UMUR, B.Sc
Department: Management Science and Engineering Programme: Economics
ISTANBUL TECHNICAL UNIVERSITY « INSTITUTE OF SOCIAL SCIENCES
OPTIMAL ENVIRONMENTAL POLICY RULE IN DIFFERENT MARKET STRUCTURES UNDER COOPERATIVE AND COMPETITIVE R&D
Master Thesis by Ilker UMUR
(412021009)
Date of submission : 08.05.2006 Date of defence examination : 02.11.2006
Supervisor : Assoc. Prof. Dr. M. Özgür KAYALICA Members of the Examining Committee : Prof. Dr. Benan Zeki ORBAY
Assoc. Prof. Dr. Ensar YILMAZ
ISTANBUL TEKNIK ÜNIVERSITESI « SOSYAL BILIMLER ENSTITÜSÜ
FARKLI PIYASA YAPILARINDA ISBIRLIKÇI VE REKABETÇI AR&GE ALTINDA OPTIMAL ÇEVRE POLITIKASI
Yüksek Lisans Tezi Ilker UMUR
(412021009)
Tezin Enstitüye Verildigi Tarih : 08.05.2006 Tezin Savunuldugu Tarih : 02.11.2006
Tez Danismani : Doç. Dr. M. Özgür KAYALICA Diger Jüri Üyeleri : Prof. Dr. Benan Zeki ORBAY
Doç. Dr. Ensar YILMAZ
PREFACE
Today environmental issues have started to sound the alarm siren. It is possible to interpret this alarm as an invitation not only for society as a whole but also for people as an individual to show the essential sensitivity to the environmental issues. From the beginning of 1980s, economists have interested intensively with environmental issues and its impact on economic activities. Due to the importance to find a panacea for an efficient use of limited resources, the inevitability of the integration of economics into policy fields has been put on the agenda. Based on such a sense, the purpose of this study is to clarify the relationship between environmental policy, environmental technology and market structure.
Initially, I would like to express my particular appreciations to my supervisor Assoc. Prof. Dr. M. Özgür KAYALICA for his guidance and support.
I am grateful to Erasmus Exchange Program and Istanbul Technical University for giving me the chance to complete my study in Universitê Louis Pasteur. I also would like to state my special thanks to Prof. Dr. Benan Zeki ORBAY and Prof. Dr. Ümit SENESEN for supporting me to benefit from Erasmus Program.
I wish to express my gratitude to my family for their trust and I am deeply indebted to my friend Gul for her aid and encouragement.
TABLE OF CONTENTS PREFACE ii LIST OF FIGURES v ÖZET vi SUMMARY vii 1. INTRODUCTION 1 2. LITERATURE REVIEW 3 2.1. Theoretical Framework 3
2.2. An Overview and Review of the Previous Studies 10
3. THE MODEL 26
3.1. Cournot Case 27
3.1.1 Under Competitive R&D 27
3.1.1.1. Stage 3 27
3.1.1.2. Stage 2 29
3.1.1.3. Stage 1 31
3.1.2 Under Cooperative R&D 34
3.1.2.1. Stage 3 34
3.1.2.2. Stage 2 35
3.1.2.3. Stage 1 37
3.2. Bertrand Case 38
3.2.1 Under Competitive R&D 38 3.2.1.1. Stage 3 38
3.2.1.2. Stage 2 39
3.2.1.3. Stage 1 41 3.2.2 Under Cooperative R&D 43 3.2.2.1. Stage 3 43
3.2.2.2. Stage 2 44
4. CONCLUSION 48
REFERENCES 50
APPENDIX A 56
APPENDIX B 66 ABOUT THE AUTHOR 79
LIST OF FIGURES Page No
Figure 2.1 Supply & Demand Curves
with External Costs 4
Figure 2.2 Abatement cost and damage
ÖZET
Bu arastirma optimal çevre politikasi yönetimini farkli pazar yapilarinda, Cournot ve Bertrand, teknolojik tasma ve ürün farklilasmasinin oldugu isbirlikçi ve rekabetçi çevresel Arastirma ve Gelistirme (Ar-Ge) altinda analiz etmektedir. Emisyon yogunlugunu azaltici Ar-Ge ve farklilastirilmis ürünün söz konusu oldugu duopol durumunda üç asamali teorik oyun teorisi dikkate alinmistir. Birinci asamada hükümet emisyon vergisi ve Ar-Ge sübvansiyonu belirler. Ikinci asamada firmalar emisyon vergisini ve Ar-Ge süb vansiyonunu veri alip eszamanli olarak Ar-Ge seviyelerini belirler. Üçüncü asamada ise iki durum analiz edilmektedir. Birinci durumda Cournot rekabeti altinda firmalar diger her seyi veri olarak alip üretim seviyelerini kararlastirir. Bununla beraber, ikinci durumda ise Bertrand rekabeti altinda firmalar diger her seyi veri olarak alip fiyat seviyelerini kararlastirir..
Her iki pazar yapisinda emisyon vergisinin marjinal hasardan az oldugu gösterilmistir. Bununla birlikte, ürün farklilasmasi yeterli derecede az oldugunda emisyon vergisi Bertrand rekabetinde marjinal hasara esitlenmektedir. Ar-Ge sübvansiyonu konusuna gelince, fiyat rekabetinde sübvansiyon her zaman pozitiftir. Miktar rekabetinde ise sübvansiyon ürün farklilasmasina ve teknolojik tasmaya dayanmaktadir; isbirlikçi Ge altinda sübvansiyon daima pozitiftir. Rekabetçi Ar-Ge ortaminda eger ürün farklilasmasi parametresi yeterince yüksek ve teknolojik tasma yeteri kadar düsükse, optimal sübvansiyon negatif olabilir. Aksi takdirde optimal sübvans iyon pozitiftir.
SUMMARY
This paper analyses optimal environmental policy rule in different market structures, Cournot and Bertrand, under cooperative and competitive environmental R&D when technologic spillover and product differentiation exist. A three-stage game theoretic model is considered in a differentiated product duopoly where R&D is emission intensity reducing. In the first stage, the regulator (government) determines emission tax and R&D subsidy. In the second stage, given the emission tax and R&D subsidy firms choose their R&D level simultaneously. In the third stage, two cases are analyzed. In the first case, firms choose their output levels taking everything else as given under Cournot competition. In the second case, however, firms choose their price levels taking everthing else as given under Bertrand competition.
It is demonstrated that emission tax is lower than marginal damage in both market structure. Nonetheless, if product differentiation is sufficiently low, emission tax is equa l to marginal damage in Bertrand competition. With regard to R&D subsidy, under price competition subsidy is always positive. Under quantity competition, subsidy depends on product differentiation and technologic spillover; subsidy is always positive under cooperative R&D. Under competitive R&D if product differentiation parameter high enough and technologic spillover parameter is sufficiently low, optimal subsidy could be negative. Otherwise, optimal subsidy is positive
1. INTRODUCTION
Since last two decades, environmental problems have increased rapidly. In the beginning of 1980s, it was realized that quantity and quality of available natural resources determine economic and social development in the long run. A change in perception in turn leads economic agents to alter their behaviour. Political parties and some employers’ organisations shift their main concern by putting the environment above work and income in their priority list. In addition, in parallel with this consciousness economists attend environmental issues (Dietz et. al., 1991).
Environmental policy has become one of the most important parts of the applied policy and theory. “It is well known that from the economists’ point of view, environmental policy is a case of analysing externalities and market failure issue thoroughly examined in microeconomic theory” (Xepapadeas, 1997).
Regarding this frame on the one hand, firms provide many different products in a large range or services to society. However, firms impose a cost on society by polluting the air, water, and land. Governments (regulators) overcome negative externality by imposing some regulation (emission tax, emission standards, quotas etc). They give subsidy to encourage firms to undertake environmental R&D as well. Concerning such strategies, a firm might respond by decreasing output level or by renovating its technology associated with production methods. Embracing Research Joint Venture (RJV) formation, the thesis weighs the probability of forming RJV under the umbrella of firms and its implications over firms.
This aspect of the thesis is assumed to bring in an insight regarding firms’ strategic behaviours. Game theory, in this respect, would serve as a brilliant tool to scrutinize strategic situations where players (firms) choose different actions in an attempt to maximize their returns while government tries to maximize welfare.
This work aims to contribute to the literature by comparing optimal environmental policy in two different markets’ conducts when firms produce
differentiated products and embrace competitive and cooperative environmental R&D.
This study includes five chapters. After providing a background in the introduction in chapter one, chapter two examines the fundamentals of environmental economics and the effects of the environmental technology as well. Moreover, previous studies about this subject are overviewed. In chapter three, a theoretical model which is used to examine our purposes is presented. The model consists of two main parts; Bertrand case and Cournot case. In chapter four, these two cases are compared. Finally in the last chapter, the results are underlined.
2. LITERATURE REVIEW
2.1. Theoretical Framework
Economic investigation of environmental policy is based on the idea that effects of destructive economic activities on the environment constitute an externality. For the precision of this thesis, externality concept should be clarified. What is externality? Externality is explained in Deardorff's Glossary of International Economics (2006) as the following: “An effect of one economic agent's actions on another, such that one agent's decisions make another better or worse off by changing their utility or cost. Beneficial effects are positive externalities; harmful ones are negative externalities.” A firm imposes a cost on society by polluting the air, water and land. The firm that owns the factory has an economic incentive to use labour or steel to the limit that it can productively employ, because those inputs are costly to the firm. Those labour and steel, which are used up in a given factory, can be assessed as a cost. This cost is internalized by the firm due to the fact that the firm has to pay for those inputs. The cost society of having some of its labour and steel used up in a given factory is internalized by the firm, because it has to pay for those inputs. Nonetheless, the firm does not have economic incentive to internalize externality of pollution.
In fact, environmental problems are due to the variance derived in between the private cost and social cost. There cannot be trade-off between environment and the production of goods under laissez- faire conditions. In this respect, it is important to recognise market failure due to externality.
Conventional pollution externality leads firms to overproduce. That’s first market failure1. Figure 2.1 below points out the effects of a negative externality. Vertical
1
It should be stated that second product market failure is caused by imperfect competition. This in turns leads to too little output.
distance between the two supply curves indicates a difference between the marginal private cost and marginal social cost. The marginal private cost is less than the
marginal social cost. In addition, it is supposed that social benefit equals to individual benefit.
Source: Wikipedia4
Figure 2.1: Supply & Demand Curves with External Costs
If the consumers take into consideration only their own private cost, they will end up at price Pp and quantity Qp, instead of the more efficient price Ps and quantity Qs. These latter reflect the idea that the marginal social benefit should equal the marginal social cost. That is to say production should be increased only if the marginal social benefit exceeds the marginal social cost. As a result, a free market is inefficient; as at the quantity Qp, the social benefit is less than the societal cost. Hence; society as a whole would be better off if the goods between Qp and Qs had not been produced. The problem is that people are buying and consuming too much.
There is a dilemma of societal communication and coordination to balance benefits and costs. This discussion also indicates that a competitive market is incapable of
4
The figure has been retrieved from World Wide Web: URL
solving pollution problem. If one of the firms decides to internalize external costs, this firm faces higher costs than those of competitors and is likely to exit the market. This situation points out that collective solution is needed; such as government intervention for restricting pollution.
The rest of this section would try to reflect different revisions of the issue with an aim to bring in an extent standpoint.
According to Pigou (1938) the social optimal level can be attained by using policy instruments. He has explained his opinion in his works “The Economics of Welfare”. In terms of his approach, the divergence between private and social costs can be made up by imposing either a tax on emission which creates environmental damages or another equivalent measure.
There is a classical example in which there is a factory generating smoke that has harmful effect on individual living nearby. According to Pigou (1938), the factory is responsible for damage; therefore, a tax should be imposed so as to reduce smoke level and environmental damage. This approach has been dared by Coase (1960). As said by Coase (1960), an optimal agreement on the level of environmental externality can be reached without any regulation. This approach is based on bargaining among pollutant and the victims of pollutions. In the example of Coase, the factory by generating pollution harms the farmer. The factory is voluntary to pay the farmer to get right of polluting because of the fact that the factory has to obtain farmer’s permission. Thus, the farmer may accept this payment in order to suffer damage implied by emissions. The optimal solution can be achieved by private negotiation. In this respect, Coase Theorem requires the existence of a well defined and enforceable property rights. In this theorem, there are only two parties and no transaction costs, which existence can prevent private bargaining. However, necessary assumptions for making the theorem valid have been found insufficient regarding the majority of environmental problems. That’s why Coase Theorem cannot be an alternative to environmental policies which are predicated on Pigovian approach (Xepapadeas, 1997).
Environmental policy tries to response the internalization of the cost of environmental degradation. Environmental policy instruments can be separated into two main groups:
a) Econo mic instruments (Subsidy, charge system, deposit refund system, tradable emission permits etc.)
b) Regulations (Standards, emission quotas, negotiations etc.)
Polluters control themselves by regarding consumption of environmental input or regulators (governments) impose limit for pollution. The relative efficiency of different policy instruments depends on specific considerations such as the regional extent of the problem, the number of pollution sources, the easiness of monitoring, the importance of transaction costs and the pervasiveness of other market distortions (Nicolaisen et al., 1991). The firms generally respond to environmental policy in different ways; by decreasing their output level or by changing production methods to decrease emission’s level.
On the contrary, some economists embrace the opinion of environmental responsibility instead of environmental taxation. One of the pioneering papers written by Bazin et al. (2004) has stated that degree of the responsibility affects environmental quality; and high degree of responsibility could be used instead of taxation. According to this paper, the fact that polluters pay a tax leads to reveal this idea: “Since I pay, I can consume and thus pollute”.
As a counter argument, also as widely held opinion, is the following: when polluters do not pay their environmental cost, this means environmental thievery and thus thievery of social welfare. In terms of Bithas (2006), environmental responsibility is necessary to form environmental behaviour; it is part of efficient environmental policy as well. But it is not enough to impede environmental thievery.
Going back to previous argument, to internalize negative externality thanks to environmental policy for the firms, marginal damage cost is equal to or greater tha n marginal abatement cost (Figure 2.2). Optimal point of emission level is where
marginal abatement cost is equal to marginal damage cost. At this point, an increase in abatement equals to the gains reduced from emissions. When marginal abatement cost is less than marginal damage cost, it leads to an excessive emission level (such as point B). In this situation, CE shows total environmental damage. The amounts to CD are internalized by the pollutants. But, the amounts to DE of environmental damage are not internalized.
Emission as a fraction of uncontrolled (laissez-faire) level
Source: Economics and environment/ a survey of issues and policy options by Joa Nicolaisen et al. (1991)
Figure 2.2: Abetment cost and damage function
According to Schwartz and Clements (1999) “From an economic perspective, main purpose of subsidies is to reallocate resources, that is, to alter economic activity and behaviour to achieve an outcome that is more desirable from what would occur otherwise. Hence, arguments for subsidies are often based on some concept of efficiency or economic justice”. On the other side, it can not be said that all subsidies are corrective in nature even if when subsidies create more desirable outcome. Compensating market imperfections is one of the reasons for using subsidies.
Subsidies is applied to case where markets do not share out resources efficiently because of the fact that owner of these resources cannot reap their full return (i.e. free rider problem). Subsidies must be paid for. Thus, it is important that subsidies are effective (i.e. reach their intended target group) and realize a given aim at minimum cost.
Subsidies are important elements for environmental policy on the subject of environmental technology. They are the main tools of innovation policy as well. In the Netherlands, empirical studies show that subsidies have a windfall gain for applicants (Kemp, 2000). Thus, it is important that subsidies should be given only if the adaptation of cleaner technology entails high costs or causes competitive disadvantage owing to more lax regulation in other country. The question “What about the effectiveness of subsidies for the development of environmentally preferable technologies?” is asked and debated by Kemp. He has studied the question with using econometric analysis on the effectiveness of thermal insulation subsidies which are given by National Insulation Program. The conclusion has approved that there is only weak a positive relationship between the subsidy for thermal home improvement and the diffusion of thermal insulation technologies. Some empirical examples are given and it is pointed out that in the Netherlands, subsidies have limited effect on environmental technology. It is underlined the conclusion of some works which have showed that innovator invest environmental technology when they believe market exist for the new technology. Investment decision is taken irrespectively of subsidies. But also it has been emphasized that it has not been studied systematically.
Firms undertake R&D with the intention of reaching desired emission level by reducing either production cost or abatement cost. Namely there are two types of R&D: production R&D and environmental R&D. In this work, environmental R&D has been taken into consideration. When governments (regulators) impose environmental policies to reduce emissions and environmental damage, which burdens extra cost for firms, costs increase while outputs decrease. Thus, strict environmental policy doesn’t adequately induce the firms to undertake
environmental R&D. Firms can form collaboration before undertaking R&D. It is called research joint venture (RJV).
As stated by Caloghirou et al. (2003), joint venture has been defined by OECD “as activities in which the operations of two or more firms are partially, but not totally, functionally integrated in order to carry out activities in one or more of the following areas: i) buying or selling operation; ii) natural resource exploration, development and/or production operations; iii) research and development operations; and iv) engineering and construction operations”. Even though there are lots of collaborations’ forms, most of them are related to technological subjects. According to Caloghirou et al. (2003), there are many works on RJVs. Two of the reasons of these works are explained in the following:
1) Growing willingness of firms to engage in cooperative R&D, which is considered as a contradiction to the idea that R&D constitutes the centre of the firms spirit, 2) RJVs are one of the applications fields for policy. If regulator perceives that RJVs are restricting the competition, it imposes policy to prevent this collaboration. Whereas policy encourages to RJVs when regulator believes the cooperation is not an obstacle to the conditions of competitive markets.
RJV can be considered as a strategic behaviour among firms. RJV raises the benefit of R&D. Veugeler (1998) clarifies RJV’s several advantages, which are in favour of firm, in the following: Sharing of costs/risks, access to partner’s know-how/markets/products, efficiency enhancements, economies of scale in production/distribution/R&D, synergy effects from exchanging/sharing complementary kno w-how, competitive considerations, monitor/control partner’s technology/markets/products, influence other alliance activities (pre-emption, followers), influence competitive structure, government policy (industrial, trade & competition policy), subsidies for co-operation, local content and anti-trust.
Anti-trust or competition laws are defined in Wikipedia Web Encyclopedia as “laws whose state purpose is the promotion of economic and business competition by prohibiting anti-competitive behaviour and unfair business practises”.
Röller et al. (1997) asked question in their works as “why firms form research joint venture?” This work underlines two main reasons in the economics literature.
(i) Internalising the spillovers associated with R&D (ii) Cost saving by sharing R&D costs.
Internalising spillovers is an effective way to overcome free-rider problem. Firms are less incentive and spend less on RJV owing to free rider behaviour. If firms form RJV with choosing R&D investment level cooperatively to maximize joint venture, spillovers are internalised and these result leads to an optimal R&D investment and raise welfare. Cost sharing also is powerful incentive as it fallows firm to pool their resources and avoid wasteful duplication. (Firms within an industry may be pursuing the same invention, using the same method and thus replicating effort). It is showed that RJVs affect market structure and market power. Moreover, large firms have less incentive to form RJV with smaller firms to increase market power. Hence, industry becomes increasingly asymmetric. In this regards, RJV may raise competitive concerns. One of the conclusions is that if firms produce similar products, they do not tend to form RJV.
Jaffe et al. (2002) has examined the relationship between technological change and environmental policy. There are two results:
1) Environmental effects on society and on economic activity are affected by the rate and the direction of technological change.
2) Environmental policy interventions generate new restraints and incentives, which affect technological development.
A development of environmental technology reduces the cost of pollution abatement and thus pollution. Environmental health is improved as well. This is a static story. But in fact there are dynamic stories between environmental policy and technology. Policies reduce pollution at present, and induce firms to invest in new technologies for the future. Development of technology changes cost/benefit analysis.
Environmental policies take this dynamic interaction into consideration. The static model does not consider the fact that technology is not free (Jaffe et al., 2004).
At this point, to understand RJV better, it should be focused on R&D market failures. There are three R&D market failures:
1) Firms take into consideration their profits more than total surplus, which in turn leads to too little R&D.
2) If one of the firms gets new technology, it does not want to share it with the other firm in the same industry. Hence, there occurs too little R&D once more.
3) Firms try to be the first to introduce new technology and therefore to capture all private benefits. This leads to over- investment in R&D.
If there is uncontrolled information leakage (spillover), firms acting independently will not internalize owing to spillover. This is called spillover effect. Thus, in the situation where there is enough (high) spillover, firms tend to under invest R&D. As Katsoulacos et al. (1999) mentions, firms cope with R&D market failure through RJV. Hence, they take R&D decision cooperatively. They handle not only spillover effect but also second and third R&D failures. But RJV is incapable of overcoming first R&D failure.
Environmental policy may induce firms to innovate either by adopting existing environmental appropriate technology or by accomplishing more and newer R&D. Even in this situation, environmental policy should consider external effect induced by innovation, market distortions in R&D market, free riding induced by R&D spillover and benefit & cost of R&D cooperation (Carraro and Metcalf, 2000). According to Ulph (1999), it can be divided five the review related about RJV: i) Performance of RJVs ii) RJVs size and membership iii) Interaction between RJVs and product market competition iv) The evaluation of RJVs and RJV policy v) Innovatio n and competition.
Chiou and Hu (2001) have examined the firms’ strategic behaviour under emission tax. In their paper, three types of environmental RJV are considered:
1) R&D cartelization in which firms choose R&D efforts to maximize the joint profit.
2) RJV competition in which firms share the R&D fruits to maximize their own profits.
3) RJV cartelization in which firms share R&D fruits and maximize the joint profit. Supposed by the model of this paper, there are two firms that produce homogenous product. These firms generate pollution. There are two different games. In the first game, a duopoly is examined without environmental RJV. The game includes two stages. In the first stage, the firms choose their pollution abatement level. In the second stage, they choose their output level. In the second game, there are three general types of RJV. The first type of RJV is the R&D cartelization. In the first stage of the second game, the two firms coordinate in the environme ntal abatement level in order to maximize their joint profit although there is no spillover of the abatement technology. In the second stage, the two firms engage in Cournot quantity competition. The second type of RJV is the RJV competition. In the first stage involving this type of RJV, the two firms spread abatement technology to each other in order to maximize their own profits; but not to attain joint profit. In the second stage, the two firms engage in Cournot quantity competition. The third type of RJV is the RJV cartelization; that is, in the first stage, the two firms share abatement technology each other in order to maximize the joint profit. Finally, in the second stage, the two firms engage in Cournot quantity competition.
This paper shows that environmental RJV doesn’t always improve the social welfare; because the firms in RJV cartelisation reduce their output level and environmental R&D level to maximize joint profits. In addition, such a cartelisation can be regarded as a social optimal when spillover is sufficiently high. Because of the fact that there is free-riding effect, an environmental RJV competition with high enough spillover coefficient will bring the lowest social surplus. A RJV cartelization has a negative
impact on the total output, on per output abatement and on social surplus. However, a RJV cartelization with a high rate of environmental technological spillover maximizes social-surplus. Thus, antitrust law enforcers should pay attention whether the members of an environmental RJV are substantially sharing environmental innovations or not. Moreover they should allow joint profit maximization to eliminate the free-riding effect. In many countries, R&D cooperation is supported under antitrust laws, which effects in promoting R&D and production efficiency exceed the inefficiency resulting from the reduction in competition.
Greenlee (2005) has studied RJV in empirically studies. It is underlined that principal benefit of RJV is accessing to the innovation venture partners. This leads to reduce cost. RJV’s structure and spillovers affect directly partner’s behaviours. When spillovers are low and joint venture membership is small, members increase R&D expenditure which is used for getting greater sales volume. Additionally benefit of the new innovations is not transmitted too largely to rivals or to partners. When spillover or number of participants increase, individual research affects overspread largely, so this in turn leads to smaller cost advantages. Thus, participant in venture invests less in R&D. But participant benefits from increased level of effective R&D thanks to sharing with additional firms. It is also found that sharing information is better for welfare than joint venture that maximizes joint profit. Under the circumstance spillovers are low, R&D sharing venture improve welfare. When there is single industry wide joint venture, it improves social welfare by increasingly total effective R&D. If there are several competing joint ventures, any collaboration reduces R&D.
Chen (2005) has examined the relation between RJV and financial structure. If cost reduction due to R&D is uncertain, the use of strategic debt in RJV competition induces the firm to high effort for in R&D. When the firms use debt, their R&D effort and output level increases. Because the firms would like to cover debt obligation through producing more and capturing a bigger market share. The use of debt weakens free rider problem. The firms do not have intensive to trick; whereas they make effort to cope with free rider problem because of strategic debt.
Furthermore, each firm’s profit is less owing to higher R&D expenditure and lower market price than in the unleveraged industry although production cost is reduced and free rider problem is weakened when the firms use debt.
In the presence of asymmetries between firms, how do the firms choose their collaboration partners? And how is important the technology of competitor? Atallah (2005) has tried to find the answers of these questions. When firms choose their partner, they consider spillover and cost differences. A firm wants to form collaboration with the most efficient firms, if low spillover exists. Cost difference between firms increases between firms; efficient firms prefer to collaborate with the most efficient firm among remaining firms. Whereas, in the situation of high spillovers, a firm prefers to remain out of collaboration but if cost differentiation is sufficiently low, firms tend to collaborate. It is also attained that larger firms with high technologic capabilities profit from R&D cooperation.
Katsoulacos and Ulph (1998) have obtained some conclusions related about RJV. Principals of them are:
i) Cost reduction is the most important reason to form RJV(eliminating duplication effort)
ii) If products are very close substitute or firms are so willingness to share information. Cost considerations tend to be dominant factor
iii) RJV might close one lab to prevent from facing very competitive situation when both firms discover.
iv) RJV may keep both of labs to get benefit of maximum when firms are different but complementary industries.
v) Eliminating needless duplication and diminishing returns of R&D expenditure are cost reasons for having two labs.
Chiroleu-Assouline et al. (2003) has compared different instruments (emission tax, emission standards and auctioned permits) of environmental policy according to the incentives for innovation and embracing of new technology when environmental technology and imperfect competition exist. In this works, it is assumed that
regulator kno ws market structure and emission level of the each firm but it is unconscious about consequence of research effort. The other assumption involves the permits to pollute, which are auctioned by government. The firms are mindful about how many permits they need with innovation or without innovation. They are also aware of the fact that the price of the permits is determined by the perfectly competitive of permits market. They have found that emission tax reduces total pollution but the innovation does not always induce to reduce pollution. If the firms adopt innovation, there are two effects for firms; decreasing in emission by reducing emission coefficient (direct effect) and reduction of environmental cost which brings on decrease production cost. This in turns increases production and emissions (indirect effect). These two effects depend on emission tax. If there are excessive taxes with innovation, pollution reduction is smaller for the situation where innovation exists than the situation on the contrary. It is underlined that three policy arguments can not be ranged on the subject of incentive to innovate, the size of innovation, acceptability of environmental policy and total welfare. Ranking depends on for a given criteria.
Montero (2002) has studied whether or not there is any difference regarding incentive to invest in environmental R&D under different market structure and environmental policy instruments.(emission standards, emission tax, tradable permits and auctioned permits). The model of the firm has two stages. In the first stage, firms choose their R&D level; in the second stage they choose their output. It is assumed that there two symmetric firms and limit of the emission level is determined exogenously. Firms’ products are strategic substitutes in Cournot competition while they are strategic complements in Bertrand competition. One of the conclusions points out that standards, emission tax or auctioned permits can procure the most incentive to invest R&D in Cournot competition. As for Bertrand competition, either tax or auctioned permits provide the most incentives. If markets are perfectly competitive, permits and emission standards have lower incentives than tax. It is emphasized that under Cournot competition, if products are strategic substitutes, under tradable permits regulation, firms have an incentive to under- invest in R&D. If
firms are in auctioned permit regulation, the firms may have incentive to over-invest in R&D.
Lee (1999) has tried to find the answer of the question that is “What is the optimal output tax for polluting oligopolistic firms?” In this work, it is assumed market structure is determined endogenously,- free entry- firms are identical and products are homogeno us. He has found that optimal tax under imperfect competitio n could be less than, equal to or greater than marginal external damage depending on curve of market demand. This conclusion is explained in that way; equilibrium number of firm could be below or above social optimum. For correcting this distortion, emission tax would be greater or less than marginal external damage. The study has emphasized that optimal tax equal to marginal external damage for symmetric oligopolists when market demand is linear.
Poyago-Theotoky (2000) has approached the relationship between environmental policy and innovation by using the argument of willingness. The firms commit more environmental R&D, sacrifice their profit and reduce production. This is qualified Voluntary Approach (V.A.). In this work, she assumed there exists duopoly and closed economy. The firms which are identical produce homogeny product. To answer the question of “What is the relation between ER&D and non-cooperative R&D and how do these formations have performance relatively in terms of environmental innovation and social welfare?” it is used three-stage game. In first stage, firms decide whether they or not form R&D organisation, in the second stage the regulator set environmental tax (as a tool of environmental policy) and in the last stage firms compete in market.
It has been attained that environmental innovation is greater in ERC than in independent R&D in the case of relatively small damage, whereas large damage opposite is true. This conclusion holds for comparison of social welfare. As for environmental tax, it is greater in the situation of independent R&D than in ERC for small damage. If there exists a large damage, the ranking is opposite.
David (2004) has compared voluntary agreement (V.A.) and emission tax as an environmental policy under Cournot competition. The regulator offers a contract to firms to limit their emission by determining specific level. The firms accept or reject. If firm refuse they must pay emission tax. While the regulator is determining emission level, he takes into consideration social welfare maximization. V.A. do not affect output always leads to higher abatement than tax. V.A. lets the firms avoid tax payment ; thus marginal production cost is reduced compared to the tax. That’s means higher output, hence consumer surplus is always higher with the V.A. V.A. lets the firms to obtain higher profit compared to tax depends on the level of threat. Nonetheless, it can not be said emission level. Because on the one hand, V.A. causes more abatement than tax on the other hand it causes highe r output and higher emissions.
Beath et al. (1998) has studied the relation between spillovers and R&D. It is showed that the effect of the spillover on the R&D depends on how significant the spillover is and what type of research is pursued. According to this study, RJV always gets a large amount of cost reduction than the independent firms and as a result spend more on R&D but, in every situation, the amount of R&D spending per unit of cost reduction lower in RJV than non cooperative R&D thanks to elimination needless duplications. In this study, R&D is separated as two stages for examining effect of the diminishing returns correct. In the first stage firms incur expenditure that will generate new knowledge while in the second stage this knowledge is enga ged to reduce unit costs. In the first stage, firms determine how many labs they use. If there is a single research path, the RJV operates one lab in order to eliminate needless duplication. If there are complementary research paths, the number of labs (one or two) depend the stage of the R&D process in which diminishing returns happen. They found that RJV operates both labs when diminishing returns occur at the first stage (creation of knowledge), whereas it will be indifferent related about the number of the labs when diminishing returns occur in the second stage (Cost reduction); because, it is proportionally more difficult to invent new technologies. It economizes a lot on physical inputs.
In the work of Poyago-Theotoky (1999), it is compared R&D competition and R&D cooperation (RJV) when spillovers are endogen. There are two identical firms which produce homogeny products and undertake cost reducing R&D. The model includes three stages. In the first stage, firms decide their R&D expenditure, in the second stage; firms decide how much of the knowledge created in the first stage and the last stage they compete in Cournot competition. The firms share full information and maximize RJV profit in RJV. To conclude, total output and the profits of the firms are higher in R&D cooperation than in R&D competition. That means consumer surplus, producer surplus and consequently welfare is more in RJV than in R&D competition. It is underlined that in the case of R&D competition, when spillover equal to zero, the profits of the firm will maximum as well. Because, positive spillover reduces rival’s unit cost and increases its market share, hence reduces its own profitability.
Albrecht (1999) has compared several environmental policy instruments including emission tax, vo luntary agreement, grandfather and auctioned permits in terms of the incentive to invest in environmental R&D. There are two sectors, polluting firms which are not identical –different marginal abatement cost-and investing firms in R&D. It has into taken considerations the decision to innovate and the marketing of the resulting innovations as endogenous. It is assumed as well that firms want to invest in innovation if the cost of innovation does not exceed a critical value which is determined the discounted profits from innovation. If the polluters are ready to pay more the price of technology, they buy and install new technology. The quantity of solving technologies depends on the effective need to reduce emission. Thus, the effects of environmental policy instruments on firms are important. If emission target is strict, that’s in turns to force the polluters to obtain new technologies which are presented by innovators. He has attained that the market created by emission tax is always more important than the market created by tradable permits. Because Tradable permits aim only to reduce emission .Moreover, it is highlighted that emission taxes is the most incentive instrument to invest in environmental R&D.
Yun et al. (2000) have studied several type R&D orga nisation including independent R&D, R&D coordination, R&D consortium and RJV in terms of technologic improvement and social welfare. In the situation of independent R&D, each firm chooses their R&D level to maximize its profit. In the case of R&D coordination firms do not share research input – output information, only corporate in deciding their R&D level. As for R&D consortium the firms share their research input – output but determine their R&D level independently. Finally, in RJV the firms share research input – output and maximize joint profit. There are two kinds of externality; positive (spillover and output sharing) and negative (input sharing). Input and output sharing are given exogenously. The analysis is performed two stage model of duopolistic competition. In the first stage, firms choose their R&D organisation and at the last stage they compete in output market. In this paper, it has been attained that either independent R&D or R&D consortium can be more effective in terms of R&D investment than R&D coordination or RJV. But it could not be stated any dominance uniquely of any form of R&D organisation which depends on spillovers, degree of competition and input-output sharing rate of R&D consortium and RJV. Such as, if the product market is competitive, independent R&D is superior to any R&D organisation. Nonetheless, if competition is weak, cooperative R&D regime may be preponderance according to technologic improvement and social welfare. In particular, when input sharing rate is relatively high, R&D consortium will be dominant to RJV.
“What can be said related to different market structures in terms of price, and welfare?”. Hackner (1999) has tried to answer this question. He allows product vertical and horizontal product differentiation. But firms have the same marginal cost of production. He has attained that Cournot price is higher than Bertrand price regardless of goods are complement or substitutes. Namely, welfare is always higher under price competition. In addition, Cournot profit is higher than Bertrand profits; whereas when products are complements, the conclusion is opposite. If there are n firms instead of two, when goods are complements and quality difference are large, low quality firms will charge higher prices under Bertrand competition than under
Cournot competition. If goods are substitutes, high quality firms might earn higher profits under Bertrand competition than under Cournot competition. He has underlined that if the model extent from two firms to n firms, the difference under two competitions disappears. Thus, in this situation, it is not clear which type of competition is more efficient.
Symeonidis (2002) has compare Bertrand case and Cournot case in a differentiated oligopoly with spillover. He has emphasized that it exists two types of differentiations; vertical and horizontal differentiation. First is due to product R&D. It implies quality differentiation and affects directly gross consumer surplus by increasing product qualities. On the other hand horizontal differentiation indicates substantiality. In the model, there are two firms which produce differentiated products. It has been described two stage game. In first stage firms choose their product R&D level and in the last stage they determine their prices or quantities. As for conclusion which has been obtained, comparative advantage depends on R&D spillover and product differentiation. R&D expenditure, price and firm’s profits are always higher under Cournot model than under Bertrand model. Moreover, output, consumer surplus and total welfare are higher in the case of Bertrand than in the case of Cournot if either R&D spillovers are weak or products are sufficiently differentiated. If R&D spillovers are strong and products are not too differentiated, output, consumer surplus and total welfare are lower in price competition than quantity competition.
Poyago-Theotoky (2003) has examined the effect of the degree of product differentiation and optimal environmental policy in Cournot competition and in Bertrand competition. As an environmental policy analzed in this paper, subsidy and emission tax are utilized on environmental R&D. The model of the paper consists of three stages. At the first stage, the government sets emission tax and environmental R&D subsidy. At the second stage, firms choose their environmental R&D level simultaneously. At the last stage, they set output or price taking as a given emission tax and R&D subsidy. This paper has showed that the emission tax is always lower than marginal damages in Cournot competition while the emission tax is generally
lower than marginal damages in Bertrand Competetion. In addition, Cournot emission tax is always lower than Bertrand emission tax. The case of nearly homogeneous products indicates that the emission tax is equal to marginal damages with price competition. Moreover, subsidy depends on the degree of product differentiation. In terms of this work’s alaysis, the optimal policy mix consists of an emission tax and a R&D subsidy. Furthermore this paper has reached the fact that if there is constrain such as linear marginal damage, the second-best tax under Bertrand competition always exceeds the second-best tax under Cournot competition.
A similar comparison for the case of the R&D subsidy reveals that whether the R&D subsidy is higher or lower in quantity or price competition depends crucially on the degree of product differentiation and on initial emissions.
Poyago-Theotoky and Petrakis (2002) have showed that when emission tax is determined exogenously, the optimal R&D subsidy can be negative depending on the degree of environmental damage and spillover parametre. Also this paper has indicated that welfare, in the case of R&D cooperation, is lower than welfare in the case of R&D subsidisation. The model of the paper is non-tournament in which there are duopoly firms producing homogenous goods under constant returns and also in which there is R&D spillover. Two different games exist. In the first game, there are three stages; at the first stage the government sets subsidy rate. At the second stage, firms choose their abatement level and how much to spend in cost reducing R&D. At the last stage, firms compete in product market by choosing their output level. Coming to the second game, subsidy doesn’t exist; firms cooperate by choosing their cost reducing R&D level in order to maximize joint profits. However, they compete in product market. It is assumed that the firms generate pollution as a by product and technology policy is exogeneous, namely emission tax is fixed.
The paper handled by Poyago-Theotoky and Petrakis (1999) has focused on the impact of two different policies; R&D subsidy and R&D cooperation in a duopoly model with cost reducing R&D, spillovers and abatement. Shortly, it can be said that the aim of this paper is to demystify the debate about which policy is better than the
other. For investigating the aim which is determined, they have used two differents model. In the first game, government sets R&D subsidy, firms choose their abatement level and firms compete in product market respectively. In the second game, firms cooperate in cost reducing R&D to maximize joint profit and compete in product market. It has been assumed that firms generate pollution as a by product, emission tax is endogenous, firms produce homogenous product. It has showed that R&D subsidy can be negative.This depends on spillover and environmental damage. The other conclusion is that welfare in the case of R&D is lower than in the case of R&D subsidization.
Katsoulacos et al. (1996) have examined that the optimal policy is a combination of R&D subsidy and emission tax when the firms generate pollution and technologic spillover exist. In the model of this paper, there are environmental R&D spillovers, pollution generating duopoly firms acting under Cournot competition and homogenous product. According to this work, the optimal tax is less than marginal damages while the subsidy depends on the deviation between emission taxes and marginal damages. It has been underlined that the firms have incentive to undertake environmental R&D only if there exists emission tax. They have found that when spillovers are sufficiently small, the optimal subsidy may be negative and when emission tax increases, output level decreases while abatement expenses increase. This work has highlighted three causes of the environmental R&D undertaken privately to deviate from social optimal R&D: i) firms do not consider consumer surplus, so they produce suboptimal output ii) Environmental spillover iii) Strategic effect. Firms tend to over- invest in environmental R&D so as to increase their market share. If the first two factors dominate over the third, optimal subsidy is positive. If spillover is small, the strategic effect dominates, and then negative subsidy should be necessary.
Poyago-Theotoky (2005) has studied the importance of environmental R&D, which is directed towards emission reduction of harmful pollutants, and which are associated with social welfare. The firms undertake R&D expenditure for reducing their emission level before the regulator sets emission tax. Namely, there is voluntary
approach for firms to reduce emissions. Regulator follows time-consistent policy. The study has focused on two different regimes related to R&D organisation:
1) Independent R&D;
2) Environmental R&D cartel.
Moreover, it has been assumed that there are spillovers in the R&D process so that a firm can benefit from the R&D effort of its rival at no cost to itself. Due to the negative externality, firms tend to over produce. So, government impose emission tax to prevent this market failure. Market structure is duopolistic. In the model, there are two scenarios. In the first scenario, there are three stages ga me. At the first stage, firms opt their environmental R&D level non-cooperatively; at the second stage, regulator sets emission tax; and at the last stage, firms compete in the market by choosing their output level. In the second scenario, firms form environmental R&D cartel at the first stage only; other stages remain the same.
This work has come to the conclusion that in the case of environmental R&D cartel (ERC), when environmental damage is low, environmental R&D is higher compared to independent R&D. If environmental damage is high, the conclusion is the opposite. The same proposition can be said about social welfare. Furthermore, this paper has paid attention to the fact that if there are n- firms in the market, which affects deeply relation of between environmental policy and the organisation of environmental R&D. Furthermore, this paper has paid attention to the fact that if there are n- firms in the market, which affects deeply the relation between environmental policy and the organisation of environmental R&D, free-rider problem would be more severe. Therefore, ERC would make more effort on environmental R&D.
Roy Chowdhruy (2002) has analyzed the interaction between environmental policy, market structure and level of the pollution. He has considered duopoly market structure where the firms endogenously decide to form joint venture. In this paper market structure is determined endogenously .Due to pollution, government imposes emission tax, which creates abatement cost for the firms. It is assumed that one firm
supplies capital while the other supplies labour in joint venture. In the model, there are two stages. At the first stage, firms decide whether to choose Cournot competition or joint venture formation. Joint venture can be formed only if two firms choose it. At the second stage, in the case of Cournot, firms simultaneously choose their output level; however, in the case of joint venture case; firms choose simultaneously the level of input supply for the joint venture. Then, the government determines optimal tax.
Two components of joint venture have been analyzed; synergy and moral hazard. If two firms form joint venture, it leads to cost reduction due to synergy. Moreover, two advantages of the joint venture ha ve been mentioned; gain from synergy and avoiding loss of rents. As for moral hazard, when the capital and labour supply reach big amount in joint venture, it’s impossible to control these labour and capital flows. Also that cannot be at the contract. The firms begin to pay attention more on their own profit than on joint venture. Thus, free rider problem appears which leads to less level of input supply than optimum. The conclusion of this work can be summarized as the following; the pollution level depends on market structure and government regulation. If government policy is strict, Cournot competition is better than joint venture formation rega rding the pollution. If the government policy is weak, joint venture formation is better than Cournot competition. Furthermore, if the synergetic effect is large, strict regulation causes an increase on the level of pollution, which leads to regime switch from joint venture to Cournot competition. For a given market structure, the optimal tax is less than marginal social damage. If the industry is not excessively polluting, by means of manipulating emission tax the first best outcome can be realized (under joint venture formation). If the industry is polluting, second best tax might or might not be equal to the optimal tax under either joint venture or Cournot competition.
Katsoulacos et al. (1999) has analyzed the impact of environmental policy on the performance of environmental RJV. In this paper, it has been examined that how environmental policy affects environmental innovation when the firms form environmental RJV. Especially it has focused on a comparison made between the
impact of environmental policy on innovative performance of RJV and non-cooperative equilibriums. In the model, two firms are considered which generate pollution by producing dirty goods. Due to environmental externality, government imposes emission tax. In line with the model, information sharing is determined endogenously besides the numbers of the lab operated endogenously. There are seven-stage in the game;
1) Government decides whether or not to allow RJV.
2) If RJVs are allowed, firms choose whether or not to form one.
3) Firms choose the number of labs to operate. At this stage, if the two firms act non-cooperatively, each of them operates their own independent lab. If they form a RJV; then, at stage 3, they can choose either to continue to operate one lab each, or to operate a single combined lab.
4) Firms choose the amount of R&D to do in each lab. At this stage, the amount of R&D is determined by the lab conditional on the probability to discover a new technology.
5) Conditioning on the outcome of the R&D decisions. Firms choose whether or not to share information. This stage depends on stage 4. There are three possibilities for the outcome of stage 4.
6) The government sets environmental taxes t00, t10, t11 conditioning on the technology that each firm has as a result of the outcomes of stages 4 and 5. In this stage, three possible situations appear depending on which technology the firms each has.
7) Firms choose output in a non-cooperative Cournot Equilibrium.
In this stage, the firms choose their output level non-cooperatively under Cournot competition.
This game has been solved by backward induction. The conclusions can be expressed as the following: Due to the failure to make the right- information-sharing decisions, to operate the right number of labs – so have excessive duplication of effort and due
to incorrect R&D decisions taken through under- or over- investment, welfare losses appear. Furthermore, it has been shown that;
a) Information-sharing is more likely when damage occurs and taxes are low.
b) When damage is low, RJVs perform better in R&D decision- making than it does under the non-cooperative equilibrium. This situation depends on two reasons. Firstly, since the returns to R&D are high, they are more likely to avoid the risk of needless duplication. Secondly, the loss occurred from under- investment of the RJV is smaller than the loss occurred from over- investment in the non-cooperative equilibrium.
c) As damage rises, the under- investment of the RJV increases and the over-investment in the non-cooperative equilibrium falls. A questionable conclusion is that RJVs do better than non-cooperative organisation when environmental damage is low; but when environmental damage is high, RJV is worse.
Oladunjoye (2005) has examined two environmental policies (subsidy and tax) under competitive R&D and under cooperative R&D organisation in a heterogeneous product market. According to the model, the firms generate pollution and face tax on emission at a rate per unit of emission in a duopoly structure and the government gives a subsidy to encourage the firms to invest in environmental R&D. There are technologic spillover and product differentiation. The model includes three stage game. In the first stage, the regulator sets a tax on emission at a rate per unit of emissions and subsidizes R&D at a rate s per unit of R&D investment. In the second stage, the firms choose their level of R&D simultaneously. In the final stage, they choose their output under Cournot competition taking the emission tax and subsidy as given by the regulator. What have been compared are the optimal emission taxes, subsidies and social welfare under both R&D arrangements.
This work has demonstrated the fact that the second-best emission tax is less than marginal damages under both environmental R&D. In addition, on the one hand, the subsidy has also been found to be strictly positive under cooperative R&D. Though, under competitive R&D it is only positive for high spillovers. On the other hand, if
spillover is low, subsidy is negative. Under the assumption of exogenous emissions tax and constant marginal damage shows that, for sufficiently low spillovers, optimal subsidy under cooperative ER&D should be greater than under competitive environmental R&D. This result also holds for high spillovers and highly differentiated products. This will discourage free riding on R&D investments among firms and it helps to reduce emission costs. Such a reduction leads to an increase on R&D levels, which minimize emissions and helps correct output market failure. However, optimal subsidy under cooperative R&D should be less than what is obtained under competitive environmental R&D for high spillovers and less differentiated products.
Using numerical computation, for sufficiently low product substitutability, optimal emission tax under environmental R&D cooperation should be less than optimal emissions tax under competitive environmental R&D; while the subsidy under cooperative environmental R&D should be more than the subsidy under competitive environmental R&D, which may be negative for low environmental R&D spillover. This will encourage the coordination of environmental R&D investments among firms while the subsidy helps to lessen environmental R&D expenditure. Thus, a decrease on expenditure gives way to an increase on environmental R&D levels that helps to correct output market failure. For sufficiently low spillover effects and high product differentiation, optimal emission tax under environmental R&D cooperation should also be lower than the optimal emission tax under environmental R&D competition; while the optimal subsidy under environmental R&D cooperation should be higher than the optimal subsidy under environmental R&D competition. However, the reverse is correct for sufficiently high spillovers and high product differentiation.
To conclude, regardless of the degree in product differentiation, if spillover is small, environmental R&D cooperation is socially desirable. Nevertheless, if there is a high spillover effect and products are less differentiated, competitive R&D is socially desirable.
3. THE MODEL
In this model, a duopoly is considered as a market where firms sell differentiated products and compete either by setting quantities or by setting prices.
j
i q
q A
P= − −γ. (1)
or direct demand function as indicated by the subsequentequation:
(
)
[
(
)
i j]
i A P P q . .1 . 1 1 2 γ γ γ − − + − = (2)where i, j = 1, 2, i.≠j and Aφ0. Parameter γ indicates the degree of product differentiation and0≤γ ≤1. The fact that y is close to zero
(
γ →0)
represents perfectly differentiated goods and local monopolist firms. If γ gets close to one(
γ →1)
, the goods become very similar (in the limit they become homogeneous). We assume that unit production costs, c, are constant while there are no fixed costs and normalizing unit costs by setting c equals to zero. The firms generate pollution by producing.Emission per unit output
j i
i e z z
e = 0 − −β. (3) i = 1, 2, i ? j, where zi represents firm i’s environmental R&D level which is directed towards emission reduction of harmful pollutants and e represents initial emissions 0 per unit of output. Additionally, β shows the degree of technological spillover between the firms.
1
0≤β ≤ and it is assumed that e0 ≥ zi +β.zj for any z and i zj. Environmental R&D expenditure for firm i, R=0,5.δ.zi2 (4)
i
z represents firm i’s environmental R&D level. The firm i has to spend an amount R to reach environmental technological level z . The symbol of i δ captures the relative efficiency of environmental R&D. It should not be ignored that environmental R&D cost function indicates diminishing returns to environmental R&D.
Total emissions can be figured as the following
(
)
∑
= + = i j i i i q e q e q e E . 1. 2. (5)To make clear the symbols, it should be said that D represents environmental damage and equals to D=
(
e1.qi +e2.qj)
φ where φ represents marginal disutility. The government has also environmental policy tools; emission tax and subsidy. Due to pollution caused by firms’ production, government imposes emission tax at a rate t per unit of emission. Futhermore, government gives subsidy at a rate s per unit of R&D investment so as to encourage the firms to invest in environmental R&D. In this model a three stage game is considered in a differentiated product duopoly where R&D is emission intensity reducing. In the first stage, the regulator (government) determines emission tax and R&D subsidy. In the second stage, given the emission tax and R&D subsidy firms choose their R&D levels simultaneously. In the third stage, two cases are analyzed. In the first case, firms choose their output levels taking everything else as given under Cournot competition. In the second case; however, firms choose their price levels taking everything else as given under Bertrand competition.3.1. COURNOT CASE
3.1.1. Under Competitive R&D 3.1.1.1. Stage 3
Given the policy scheme (t,s) announced by the governments and the choice of R&D effort in emission reduction z , firm i maximizes following profit by choosing its i output level;
( )
2(
)
( )
2 . . 5 , 0 . 1 . . . . . . 5 . 0 . 1 . . . i i i i i j i i i i i Pq te q s δ z A q γ q q te q s δ z π = − − − = − − − − − (6)The first order condition is obtained as follows,
2 . . 0 . . . 2 i j i i i j i i A te q q e t q q A q γ γ π − − = ⇒ = − − − = ∂ ∂ (7)
The reaction functions are obtained as follows,
(
)
2 . . . 0 i j j i q z z e t A q = − − −β −γ (8a)(
)
2 . . . 0 j i i j q z z e t A q = − − −β −γ (8b)Solving simultaneously eq.(8a) and (8b) Cournot-Nash eq.output levels are obtained as follows,
(
)(
) (
)
(
)
2 0 4 . . . 2 . . . 2 . . 2 γ γ β β γ γ − − + − + − − = ∗ i j i z t z t e t A q ,{ }
i, j ={ }
1,2 , i ≠ j (9) ∗ i( )
2 2 . . 1 . 5 , 0 i i i q s δ z π = − − πiis overall profit. 5 (10) 3.1.1.2. Stage 2In the second stage firm i taking the subsidy on R&D as given will max second stage profit by choosing z . i 6
( )
2 2 . . 1 . 5 , 0 i i i q s δ z π = − −The first order condition is obtained as follows,
( )
1 . . 0 . . 2 0 − − = ∂ ∂ ⇒ = ∂ ∂ i i i i i i s z z q q z δ πIn the symmetric equilibrium zi = zj = zccomp, the solution related to R&D effort can be expressed in the following way;7
(
)(
)(
)
ccomp ccomp e t A t z Ω − − − = 2..2 γ.β .2 γ . . 0 (11) where Ωccomp =[
( )
1−s.δ.(
4−γ 2)
2 −2.t2.(
2−γβ)(
.2−γ)(
.β +1)
]
5See in the appendix (A1)
6 The second order condition requires 2
(
)
2(
)
(
2)
24 . 1 . 2 . 2 t − γ β π − s δ − γ while the
stability condition is satisfied for
( )( )( ) ( )
(
2)
22 2 . . 1 . 2 1 . . 4
.
2 t − γ β β + − γ π − s δ − γ or Ωccomp φ 0 7
